You'd presumably have to budget for it. I don't think those proposing the idea have taken that into consideration, so its an important issue to raise. You'd need something other than military service to justify the investment, I think.
You'd need to train more drill instructors. With some planning, and the transition to universal enlistment being at a defined future date, you could have the additional drill instructors trained and ready by the start date of the new program.
You'd need more than military service. It would need to be something with tangible public benefit, like a CCC style civilian projects, akin to the civilian service in Germany, or the road and town building that Roman soldiers did when not fighting.
Alternative, if it involved some education (community college level courses, for example, vocational training, etc), that could tangibly increase the productivity of the youth exiting it, then the increased earning potential (and thus taxable income) would offset the costs in the long run.
Or both.
The concern is the hammer and nail proposition. You don't build a big ******* hammer unless you plan on smashing a few nails. And massively increasing the size of our military could lead to more wars, as we need to justify the expense.
They'd get exemptions like Captain Bonespurs.